The arterial vascular system exchanges blood gases using pulmonary
capabilities. In humans, hemodynamic flows are subjected to periodic
velocity modulations. Fluid mechanics and transport of blood gases play
an important role in understanding how constitutive relations of the
arterial system contribute to human functioning within physiological
limits. Assuming the hemodynamic system as a finite dissipative system,
the nonlinear evolution equation is perused to understand dynamical
challenges under physiological conditions. The infinitesimal component
of the vessel wall with concentric thickening in tunica media is
considered as a nonaxisymmetric bulge in an elastic-compliant artery.
Using the Lie group of transformations method, we discuss the
implications of traveling wave solutions to describe their impact on
hemodynamic flow in an elastic-compliant artery. We find that cumulative
accretion of potential energy contributes to the creation of bright
soliton at the apex of the bulge. The wave speed is maximum at the peak
of the bulge and progressively retards with the antegrade flow.